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NASA NTRS2012

Numerical Study of Pressure Fluctuations due to High-Speed Turbulent Boundary Layers

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by fully developed turbulence in supersonic turbulent boundary layers with an emphasis on both pressure fluctuations at the wall and the acoustic fluctuations radiated into the freestream. The wall and freestream pressure fields are first analyzed for a zero pressure gradient boundary layer with Mach 2.5 and Reynolds number based on momentum thickness of approximately 2835. The single and multi-point statistics reported include the wall pressure fluctuation intensities, frequency spectra, space-time correlations, and convection velocities. Single and multi-point statistics of surface pressure fluctuations show good agreement with measured data and previously published simulations of turbulent boundary layers under similar flow conditions. Spectral analysis shows that the acoustic fluctuations outside the boundary layer region have much lower energy content within the high-frequency region. The space-time correlations reflect the convective nature of the pressure field both at the wall and in the freestream, which is characterized by the downstream propagation of pressure-carrying eddies. Relative to those at the wall, the pressure-carrying eddies associated with the freestream signal are larger and convect at a significantly lower speed. The preliminary DNS results of a Mach 6 boundary layer show that the pressure rms in the freestream region is significantly higher than that of the lower Mach number case.

Duan, Lian↗

DOE OSTI2023

Generalized analytical and numerical modeling of optical second harmonic generation in anisotropic crystals and complex heterostructures using #SHAARP package

Optical second harmonic generation (SHG) is a nonlinear optical effect widely used for nonlinear optical microscopy and laser frequency conversion. The closed-form analytical solution of the nonlinear optical responses is essential for evaluating the optical responses of new materials whose optical properties are unknown a priori. Many approximations have therefore been employed in the existing analytical approaches, such as slowly varying approximation, weak reflection of the nonlinear polarization, transparent medium, high crystallographic symmetry, Kleinman symmetry, easy crystal orientation along a high-symmetry direction, phase matching conditions and negligible interference among nonlinear waves, which may lead to large errors in the reported material properties. To avoid these approximations, here we have developed an open-source package named Second Harmonic Analysis of Anisotropic Rotational Polarimetry (#SHAARP) for single interface (si) and in multilayers (ml) for homogeneous crystals. The reliability and accuracy are established by experimentally benchmarking with both the SHG polarimetry and Maker fringes predicted from the package using standard materials. SHAARP.si and SHAARP.ml are available through GitHub https://github.com/Rui-Zu/SHAARP and https://github.com/bzw133/SHAARP.ml, respectively.

complex systems↗

DOE OSTI2023

Closed Loop Geothermal Working Group: GeoCLUSTER App, Subsurface Simulation Results, and Publications

To better understand the heat production, electricity generation performance, and economic viability of closed-loop geothermal systems in hot-dry rock, the Closed-Loop Geothermal Working Group -- a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed-loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and supercritical CO2) while varying seven continuous independent parameters of interest (mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying Python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the techno-economic analysis script are provided. This data submission will contain results from the Closed Loop Geothermal Working Group study that are within the public domain, including publications, simulation results, databases, and computer codes. GeoCLUSTER is a Python-based web application created using Dash, an open-source framework built on top of Flask that streamlines the building of data dashboards. GeoCLUSTER provides users with a collection of interactive methods for streamlining the exploration and visualization of an HDF5 dataset. The GeoCluster app and database are contained in the compressed file geocluster_vx.zip, where the "x" refers to the version number. For example, geocluster_v1.zip is Version 1 of the app. This zip file also contains installation instructions. **To use the GeoCLUSTER app in the cloud, click the link to "GeoCLUSTER on AWS" in the Resources section below. To use the GeoCLUSTER app locally, download the geocluster_vx.zip to your computer and uncompress this file. When uncompressed this file comprises two directories and the geocluster_installation.pdf file. The geo-data app contains the HDF5 database in condensed format, and the GeoCLUSTER directory contains the GeoCLUSTER app in the subdirectory dash_app, as app.py. The geocluster_installation.pdf file provides instructions on installing Python, the needed Python modules, and then executing the app.

15 GEOTHERMAL ENERGY↗

NASA NTRS1994

Buckling and vibration analysis of laminated panels using VICONOPT

The analysis aspects of the 23,000-line FORTRAN program VIPASA with constraints and optimization (VICONOPT) are described. Overall stiffness matrices assembled from the earlier exact vibration and instability of plate assemblies including shear and anisotropy (VIPASA) flat plate stiffnesses are optionally coupled by Langrangian multipliers to find critical buckling loads, or natural frequencies of undamped vibration, of prismatic assemblies of anisotropic flat plates with arbitrarily located point supports or simple transverse supporting frames. The longitudunal continuity of typical wing and fuselage panels is closely approximated because the solutions are for the infinitely long structure obtained by repeating a bay and its supports longitudinally. Any longitudinally invariant in-plane plate stresses are permitted, and very rapid solutions are guaranteed by numerous refinements, including multilevel substructuring and a method for repetitive cross sections that is exact for regular polygons used to represent cylinders. Modal displacements and stresses in or between plies of laminated plates are calculated and plotted, with values being recovered at all nodes of substructures. Comparison with usual approximate finite-element methods confirms that, for comparably converged solutions, VICONOPT is typically between 100 and 10(exp 4) times faster.

Kennedy, David↗

NASA NTRS1995

A k-Omega Turbulence Model for Quasi-Three-Dimensional Turbomachinery Flows

A two-equation k-omega turbulence model has been developed and applied to a quasi-three-dimensional viscous analysis code for blade-to-blade flows in turbomachinery. the code includes the effects of rotation, radius change, and variable stream sheet thickness. The flow equations are given and the explicit runge-Kutta solution scheme is described. the k-omega model equations are also given and the upwind implicit approximate-factorization solution scheme is described. Three cases were calculated: transitional flow over a flat plate, a transonic compressor rotor, and transonic turbine vane with heat transfer. Results were compared to theory, experimental data, and to results using the Baldwin-Lomax turbulence model. The two models compared reasonably well with the data and surprisingly well with each other. Although the k-omega model behaves well numerically and simulates effects of transition, freestream turbulence, and wall roughness, it was not decisively better than the Baldwin-Lomax model for the cases considered here.

Chima, Rodrick V.↗

DOE OSTI2021

Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation

This paper details the modeling pipeline and validates the baseline analysis choices of the DES Year 3 joint analysis of galaxy clustering and weak lensing (a so-called "3$\times$2pt" analysis). These analysis choices include the specific combination of cosmological probes, priors on cosmological and systematics parameters, model parameterizations for systematic effects and related approximations, and angular scales where the model assumptions are validated. We run a large number of simulated likelihood analyses using synthetic data vectors to test the robustness of our baseline analysis. We demonstrate that the DES Year 3 modeling pipeline, including the calibrated scale cuts, is sufficiently accurate relative to the constraining power of the DES Year 3 analyses. Our systematics mitigation strategy accounts for astrophysical systematics, such as galaxy bias, intrinsic alignments, source and lens magnification, baryonic effects, and source clustering, as well as for uncertainties in modeling the matter power spectrum, reduced shear, and estimator effects. We further demonstrate excellent agreement between two independently-developed modeling pipelines, and thus rule out any residual uncertainties due to the numerical implementation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Neutron diffusion calculation in heterogeneous geometry based on local/global iteration using proper orthogonal decomposition

This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1983

The growth of the tearing mode - Boundary and scaling effects

A numerical model of resistive magnetic tearing is developed in order to verify and relate the results of the principal approximations used in analytic analyses and to investigate the solutions and their growth-rate scalings over a large range of primary parameters which include parametric values applicable to the solar atmosphere. The computations cover the linear behavior for a variety of boundary conditions, emphasizing effects which differentiate magnetic tearing in astrophysical situations from that in laboratory devices. Eigenfunction profiles for long and short wavelengths are computed and the applicability of the 'constant psi' approximation is investigated. The growth rate is computed for values of the magnetic Reynolds number up to a trillion and of the dimensionless wavelength parameter down to 0.001. The analysis predicts significant effects due to differing values of the magnetic Reynolds number.

Steinolfson, R. S.↗

NASA NTRS1994

Analysis and prediction of ocean swell using instrumented buoys

During the period 20-23 September 1990, the remnants of Supertyphoon Flo moved into the central North Pacific Ocean with sustained wind speeds of 28 m/s. The strong wind and large fetch area associated with this storm generated long-period swell that propagated to the west coast of North America. National Data Buoy Center moored-buoy stations, located in a network that ranged from the Gulf of Alaska to the California Bight, provided wave spectral estimates of the swell from this storm. The greatest dominant wave periods measured were approximately 20-25 s, and significant wave heights measured ranged from 3 to 8 m. Wave spectra from an array of three nondirectional buoys are used to find the source of the long-period swell. Directional wave spectra from a heave-pitch-roll buoy are also used to make an independent estimate of the source of the swell. The ridge-line method, using time-frequency contour plots of wave spectral energy density, is used to determine the time of swell generation, which is used with the appropriate surface pressure analysis to infer the swell generation area. The diagnosed sources of the swell are also compared with nowcasts from the Global Spectral Ocean Wave Model of the Fleet Numerical Oceanography Center. A simple method of predicting the propagation of ocean swell, by applying a simple kinematic model of wave propagation to the estimated point and time source, is demonstrated.

Mettlach, Theodore↗

DOE OSTI2023

Tabulated Database of Closed-Loop Geothermal Systems Performance for Cloud-Based Technical and Economic Modeling of Heat Production and Electricity Generation: Preprint

To better understand the heat production, electricity generation performance and economic viability of closed loop geothermal systems in hot-dry-rock, the Closed Loop Geothermal Group, a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and super-critical CO2) while varying seven continuous independent parameters of interest (i.e., mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an Organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the TEA (techno-economic analysis) script are provided.

co-axial↗

DOE OSTI2021

Unraveling the implications of finite specimen size on the interpretation of dynamic experiments for polycrystalline aluminum through direct numerical simulations

Normal and Pressure-shear plate impact (NPI and PSPI) experiments are popular experimental techniques for studying the mean-field macroscopic behavior of polycrystalline metals under high-rate dynamic loading. However, since both configurations rely upon geometry for subjecting the specimen to high strain rates, these experiments often involve a limited specimen size. Moreover, because of the inherent heterogeneities present within polycrystalline metals, it is difficult to ascertain if the size of the specimen and/or regions where measurements are made are sufficiently large for making representative inferences about the mean-field macroscopic properties from single-point velocity measurements. In the present study, we quantify the expected measurement variability on observable point measurements in NPI and PSPI experiments by carrying out direct numerical simulations (DNS) of statistically representative polycrystalline microstructures subjected to dynamic compression and compression-shear loading. In particular, we consider the role of specific material heterogeneities (e.g. the grain-to-grain difference in size, crystallographic orientation) on dispersion in the normal and transverse particle velocity records and on local fluctuations in key state variables (e.g. velocity, accumulated plastic strain) by incorporating these effects directly into a representative synthetic microstructure geometry and crystalline description of pure polycrystalline aluminum. The form of the present study is a large parametric investigation, consisting of ten ensembles of one hundred simulations. Each of the thousand simulations reflects a randomly realized synthetic microstructure in one of five cases of decreasing average grain size for the two loading configurations. Our analysis of the DNS results demonstrates that for both of these experimental configurations, the grain size directly correlates with the coefficient of variation (CV) in simulated point measurements, showing a convergent decrease in CV to zero (i.e. particle velocity record approaches the mean-field value) with decreasing grain size. Remarkably, the magnitude of variations in the particle velocity record is shown to be largest where the deviatoric stresses are most significant. In the case of NPI, this occurs at the elastic and plastic wavefront, whereas, in the case of PSPI, the magnitude of fluctuations are approximately constant throughout the experimental window time. The reasoning for the scatter in particle velocity due to the heterogeneous microstructure is demonstrated to be dependent on the mechanisms for accommodating deformation and on the interaction of reflection waves generated at sites of heterogeneities occurring at the scale of grains. Lastly, we develop a power-law description for the magnitude of scattering versus characteristic length, which provides a statistical framework for assessing the required number of grains per characteristic specimen dimension for minimizing scatter within these two experimental configurations (NPI, PSPI).

36 MATERIALS SCIENCE↗

DOE OSTI2021

Bayesian model averaging for analysis of lattice field theory results

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be considered for the same lattice data. Model averaging, which amounts to a probability-weighted average over all model variations, can incorporate systematic errors associated with model choice without being overly conservative. We discuss the framework of model averaging from the perspective of Bayesian statistics, and give useful formulae and approximations for the particular case of least-squares fitting, commonly used in modeling lattice results. In addition, we frame the common problem of data subset selection (e.g. choice of minimum and maximum time separation for fitting a two-point correlation function) as a model selection problem and study model averaging as a straightforward alternative to manual selection of fit ranges. Numerical examples involving both mock and real lattice data are given.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids. LDRD Final Report

This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. In this project, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality. At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5x improvement in accuracy and allows for taking an 8x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method. The report concludes with a brief summary of ongoing projects and collaborations that utilize or extend the products of this work.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

On the numerical solution of the dynamically loaded hydrodynamic lubrication of the point contact problem

The transient analysis of hydrodynamic lubrication of a point-contact is presented. A body-fitted coordinate system is introduced to transform the physical domain to a rectangular computational domain, enabling the use of the Newton-Raphson method for determining pressures and locating the cavitation boundary, where the Reynolds boundary condition is specified. In order to obtain the transient solution, an explicit Euler method is used to effect a time march. The transient dynamic load is a sinusoidal function of time with frequency, fractional loading, and mean load as parameters. Results include the variation of the minimum film thickness and phase-lag with time as functions of excitation frequency. The results are compared with the analytic solution to the transient step bearing problem with the same dynamic loading function. The similarities of the results suggest an approximate model of the point contact minimum film thickness solution.

Lim, Sang G.↗

DOE OSTI2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2005

A Concept for the Inclusion of Analytical and Computational Capability in Existing Systems for Measurement of Neutron Flux

For approximately two decades, efforts have been sponsored by NASA's Marshall Space Flight Center to make possible high-speed, automated classification and quantification of constituent materials in various harsh environments. MSFC, along with the Air Force/Arnold Engineering Development Center, has led the work, developing and implementing systems that employ principles of emission and absorption spectroscopy to monitor molecular and atomic particulates in gas plasma of rocket engine flow fields. One such system identifies species and quantifies mass loss rates in H2/O2 rocket plumes. Other gases have been examined and the physics of their detection under numerous conditions were made a part of the knowledge base for the MSFC/USAF team. Additionally, efforts are being advanced to hardware encode components of the data analysis tools in order to address real-time operational requirements for health monitoring and management. NASA has a significant investment in these systems, warranting a spiral approach that meshes current tools and experience with technological advancements. This paper addresses current systems - the Optical Plume Anomaly Detector (OPAD) and the Engine Diagnostic Filtering System (EDIFIS) - and discusses what is considered a natural progression: a concept for migrating them towards detection of high energy particles, including neutrons and gamma rays. The proposal outlines system development to date, basic concepts for future advancements, and recommendations for accomplishing them.

Patrick, Clinton↗

NASA NTRSDate not supplied

On A Stabilization of the Ingard-Myers Impedance Boundary Condition

It has been well-known that the Ingard-Myers impedance condition, while simple to apply, is subject to the hydrodynamic Kelvin-Helmholtz instability due to its use of a vortex sheet in modeling the flow at the liner boundary. Recently, in the development of a time domain boundary element method for acoustic scattering by treated surfaces, it was found that by neglecting a certain second-order spatial derivative term in the Ingard-Myers formulation, the hydrodynamic instability can be avoided. The present paper aims to provide further analysis of this modified condition, hereby referred to as Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC). It will be shown, based on the dispersion relations of linear waves, that the instability intrinsic to the Ingard-Myers condition is eliminated in the proposed new formulation. Quantitative assessments on the accuracy of TIMIBC for scattering of acoustic waves by lined surfaces will be carried out, and its effectiveness will be demonstrated by numerical examples. Specifically, the accuracy is assessed by comparing solutions obtained by the Ingard-Myers condition with that by the proposed TIMIBC where theoretical reflection coefficients at a lined surface are derived for cases of plane and spherical incident waves. It is found that the TIMIBC provides a good approximation to the original Ingard-Myers condition for flows of low to mid subsonic Mach numbers. Time domain implementations of TIMIBC are also discussed and illustrated with a numerical example using a finite difference scheme. As many studies have shown the Ingard-Myers condition to be the correct limit of boundary layer thickness going to zero, the proposed TIMIBC can offer a practical solution for overcoming the intrinsic instability associated with the Ingard-Myers condition.

Time Domain BEM↗

NASA NTRSDate not supplied

On A Stabilization of the Ingard-Myers Impedance Boundary Condition

Time Domain BEM↗